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Q3.

Expert-verifiedFound in: Page 302

Book edition
Student Edition

Author(s)
Carter, Cuevas, Day, Holiday, Luchin

Pages
801 pages

ISBN
9780078884801

**Solve each inequality. Then graph it on a number line.**

**$p-4<-7$**

The required value of *x* is $\left(-\infty ,-3\right)$. The graph on the number line is,

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\le \text{or}\ge $, use the bracket or a solid circle at that endpoint.

Properties of inequality:

$1.\text{}b\le c\Rightarrow b\pm a\le c\pm a\phantom{\rule{0ex}{0ex}}2.\text{}b\le c\Rightarrow ab\le ac,\text{if}a>0\phantom{\rule{0ex}{0ex}}3.\text{}b\le c\Rightarrow ab\ge ac,\text{if}a<0$

In order to solve the inequality:

$p-4<-7$

Add 4 both sides of the inequality, as

$p-4<-7\phantom{\rule{0ex}{0ex}}p-4+4<-7+4\phantom{\rule{0ex}{0ex}}p<-3$

Thus, the solution of the given inequality is every number is strictly less than $-3$, this can be represented in the interval form, as width="69" style="max-width: none; vertical-align: -4px;" $\left(-\infty ,-3\right)$.

Now, in order to sketch the graph of the solution of the inequality, since the interval of solution at left end point $-3$ is strict, so use a hollow circle at point $-3$. And the solution interval at left endpoint $-\infty $, thus every point strictly less than $-3$ is in the solution interval of given inequality. The graph of the solution of inequality is shown below:

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